Problems2450_07 - PROBLEMS FOR ECON 2450 Preliminary,...

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Unformatted text preview: PROBLEMS FOR ECON 2450 Preliminary, continuously updated Nippe Lagerl&f March 17, 2008 1 Introduction To be written. A The IS-LM and Mundell-Fleming models Problem A.1 Consider an IS-LM model where consumption, C , is given by the following consumption function: C ( Y & T ) = a + b ( Y & T ) . (1) where a > and < b < 1 . (a) Graph C , as given by the function in (1), in a diagram with Y on the horizontal axis. Which is the lowest level of income ( Y ) that is consistent with non-negative consumption? Now, let taxes be a function of income: T = &Y , (2) where < & < 1 . (b) How does your answer under (a) change when taxes are given by (2)? 1 Recall that the IS curve is given by combinations of r and Y that satisfy Y = C ( Y & T ) + I ( r ) + G: (3) (c) Use (1), (2), and (3) to &nd an expression for the slope of the IS curve (as drawn in a diagram with r on the vertical axis and Y on the horizontal axis). That is, &nd an expression for dr dY along the IS curve. (d) We know that I ( r ) < . What does your answer under (c) imply about the slope of the IS curve? (Is it positive or negative?) Now let the investment function be given by I ( r ) = &r & & , (4) where & > and > . (e) Say that we think that investment cannot be negative. Then why would the investment function in (4) be more reasonable than a linear one? (f) Derive an expression for the IS curve when investment is given by (4). Your answer should be an equation with r on the left-hand side, and Y and exogenous parameters on the right-hand side. (g) Draw the graph of the IS curve derived under (f). You will &nd that points on the IS curve cannot fall below some level of Y . ( Hint: r goes to in&nity as Y approaches that level from above.) Derive an expression for that minimum level, and explain intuitively why Y cannot fall below it. Problem A.2 Consider the so-called Mundell-Fleming (or IS*-LM*) model, which describes a small open economy. The exchange rate, denoted e , is the amount of foreign currency, say = Y (Japanese yen), that one must pay to buy one unit of the domestic currency, say $. A high e thus means that the domestic currency is expensive: foreign- ers pay a lot for the domestic currency, and domestic agents pay little for the foreign currency. Let P f be the price of foreign goods, and P d the price of domestic goods. Also, let be the spending share on domestic goods in the consumption 2 basket of the typical consumer in the domestic country, and 1 & & the spending share on foreign goods, where < & < 1 . (a) To the domestic consumer the price of a foreign good in terms of the domestic currency is P f =e . Explain why. This means that the general price level in $ in the domestic country, P , is given by P = &P d + (1 & & ) P f e . (5) The domestic interest rate is &xed and equal to the exogenous world interest rate, r & . Like in the IS-LM model, demand for real money balances is given by L ( r & ;Y ) , which now depends on only one endogenous variable, Y . Recall that @L (...
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Problems2450_07 - PROBLEMS FOR ECON 2450 Preliminary,...

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